Cho a, b, c, d >0. CMR:

\(\sqrt{\left(a+b\right)\left(c+d\right)}\ge\sqrt{ac}+\sqrt{bd}\)

\(Cho\) \(y>0,\) x là số thực bất kì. CMR:

\(\dfrac{x^6+y^9}{4}\ge3x^2y^3-16\)

\(Cho\) \(x,y,z>0.CMR:\)

\(x+\dfrac{1}{\left(x-y\right)y}\ge3\)

\(Cho\) \(a,b,c>0.CMR:\)

\(\left(a+b+c\right)\left(a^2+b^2+c^2\right)\ge9abc\)

\(Cho\) \(a,b,c\ge0.CMR:\)

\(a+b+c\ge\dfrac{3}{2}\sqrt[3]{\left(a+b\right)\left(b+c\right)\left(c+a\right)}\)

CMR : \(\dfrac{a^2+2}{\sqrt{a^2+1}}\ge với\forall a\)

Cho a, b, c \(\ge\dfrac{-3}{4}\) và a + b + c + d = 3. CMR: \(\sqrt{4a+3}+\sqrt{4b+3}+\sqrt{4c+3}\le3\sqrt{7}\)

Giải các phương trình sau :

\(\sqrt{x^2+6}=x-2\sqrt{x^2-1}\)

Giải các phương trình sau :

\(\sqrt{1-\sqrt{x^2-x}}=\sqrt{x}-1\)

Put in the right prepositions.

1. Was there anything good ___ TV last night ?

2. Remote controls are used to interact ___ TV.

3. I prefer sport programs ___ others, but there are no sports programs ___ Saturday afternoon.